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학술연구/단체지원/교육 등 연구자 활동을 지속하도록 DBpia가 지원하고 있어요.
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논문 기본 정보
- 자료유형
- 학술저널
- 저자정보
- 발행연도
- 2023.1
- 수록면
- 243 - 256 (14page)
- DOI
- 10.4134/CKMS.c220009
이용수
초록· 키워드
오류제보하기
We deal with a type of inverse pseudo-orbit tracing property with respect to the class of continuous methods, as suggested and studied by Pilyugin \cite{P1}. In this paper, we consider a continuous method induced through the diffeomorphism of a compact smooth manifold, and using the concept, we proved the following: (i) If a diffeomorphism $f$ of a compact smooth manifold $M$ has the robustly pointwise inverse pseudo-orbit tracing property, $f$ is structurally stable. (ii) For a $C^1$ generic diffeomorphism $f$ of a compact smooth manifold $M$, if $f$ has the pointwise inverse pseudo-orbit tracing property, $f$ is structurally stable. (iii) If a diffeomorphism $f$ has the robustly pointwise inverse pseudo-orbit tracing property around a transitive set $\Lambda$, then $\Lambda$ is hyperbolic for $f$. Finally, (iv) for $C^1$ generically, if a diffeomorphism $f$ has the pointwise inverse pseudo-orbit tracing property around a locally maximal transitive set $\Lambda$, then $\Lambda$ is hyperbolic for $f$. In addition, we investigate cases of volume preserving diffeomorphisms.
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